The government is to launch a controversial broadside against 'elitist' private schools, saying that many do not justify their charitable status.

In a signal to Labour's core voters, Alan Johnson, the Education Secretary, will warn that Britain's biggest and wealthiest independent schools should do more to share their teachers and facilities with children in the wider community if they are to keep their status as charities - which is crucial because it allows them to avoid tax on donations, saving them up to £100m a year. The sector should also do more to help poorer parents pay their children's fees.

The tax break, effectively a public subsidy for private schools, has long been resented by Labour MPs, but the schools insist that without it many smaller establishments could be forced to close. Fees would also have to rise, putting private education out of reach of more people.

Johnson's words will be seen as an olive branch to Labour rebels who are threatening to ambush charities legislation now going through Parliament, in an attempt to make it harder for schools to get charitable status. His intervention is also likely to strengthen his position in any future contest for the post of Labour's deputy leadership.

He let slip his views under questioning by the Commons education select committee last week. While private schools must demonstrate 'public benefit' in order to qualify for charitable status, he is understood to believe that too many schools get away with minimal efforts, such as occasionally letting local schools play on their sports pitches or offering a few individual bursaries.

'The rules should be applied in such a way that they make full use of their best assets, not just land and facilities but their teachers,' said a source close to Johnson. 'They have some of the best maths, science and foreign language teachers in the country and they are really good at getting the most out of gifted pupils. Those are things the state sector could use. The schools with the greatest resources should be expected to do most to meet the test.'

In a speech tomorrow to the UK Youth Parliament, Johnson is expected to say he wants independent schools to work more closely with the state sector, with the best-resourced doing most to improve children's life chances in the wider community.

The move puts David Cameron, the Eton-educated Conservative leader, in the difficult position of having to choose between either attacking the kind of education from which he benefited or being painted as elitist by Labour MPs.

Rebels will this week table an amendment to the charities bill, expected to be backed by 50 Labour MPs plus the Liberal Democrats, which would require the Charities Commission to heed any 'undue restrictions' on people being able to benefit from a given charity. This would require them to be tougher on the schools that charge the highest fees.

Johnson will not yet back changes to the bill, with the Cabinet Office adamant that it is tough enough. But his words were welcomed by Labour rebels. 'If a school is charging high fees, it should be doing much more than perhaps letting the local comprehensive use its football pitch once a year,' said John Grogan, the MP for Selby. 'It is encouraging news that the Education Department takes a progressive view and I would hope now that the Cabinet Office would rethink.'

Barry Sheerman, the select committee chairman, said: 'He [Johnson] was saying that if private schools who had charitable status didn't act like charities, we would have to look at this. It still seems to me that the [rules governing the] charitable status for certain schools that we are talking about is very loose.'